Elasticity

Theory, Applications, and Numerics

4th Edition - March 25, 2020
Imprint: Academic Press
Author: Martin H. Sadd
Language: English
Paperback ISBN:
9 7 8 - 0 - 1 2 - 8 1 5 9 8 7 - 3
eBook ISBN:
9 7 8 - 0 - 1 2 - 8 1 5 9 8 8 - 0

Elasticity: Theory, Applications, and Numerics, Fourth Edition, continues its market-leading tradition of concisely presenting and developing the linear theory of elasticity, mo… Read more

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Elasticity: Theory, Applications, and Numerics, Fourth Edition, continues its market-leading tradition of concisely presenting and developing the linear theory of elasticity, moving from solution methodologies, formulations, and strategies into applications of contemporary interest, such as fracture mechanics, anisotropic and composite materials, micromechanics, nonhomogeneous graded materials, and computational methods.

Developed for a one- or two-semester graduate elasticity course, this new edition has been revised with new worked examples and exercises, and new or expanded coverage of areas such as treatment of large deformations, fracture mechanics, strain gradient and surface elasticity theory, and tensor analysis. Using MATLAB software, numerical activities in the text are integrated with analytical problem solutions. Online ancillary support materials for instructors include a solutions manual, image bank, and a set of PowerPoint lecture slides.

Cover image
Title page
Table of Contents
Copyright
Preface
Acknowledgments
About the Author
Part 1. Foundations and elementary applications
Chapter 1. Mathematical preliminaries
1.1. Scalar, vector, matrix, and tensor definitions
1.2. Index notation
1.3. Kronecker delta and alternating symbol
1.4. Coordinate transformations
1.5. Cartesian tensors
1.6. Principal values and directions for symmetric second-order tensors
1.7. Vector, matrix, and tensor algebra
1.8. Calculus of Cartesian tensors
1.9. Orthogonal curvilinear coordinates
Chapter 2. Deformation: Displacements and strains
2.1. General deformations
2.2. Geometric construction of small deformation theory
2.3. Strain transformation
2.4. Principal strains
2.5. Spherical and deviatoric strains
2.6. Strain compatibility
2.7. Curvilinear cylindrical and spherical coordinates
Chapter 3. Stress and equilibrium
3.1. Body and surface forces
3.2. Traction vector and stress tensor
3.3. Stress transformation
3.4. Principal stresses
3.5. Spherical, deviatoric, octahedral, and von Mises stresses
3.6. Stress distributions and contour lines
3.7. Equilibrium equations
3.8. Relations in curvilinear cylindrical and spherical coordinates
Chapter 4. Material behavior—linear elastic solids
4.1. Material characterization
4.2. Linear elastic materials—Hooke's law
4.3. Physical meaning of elastic moduli
4.4. Thermoelastic constitutive relations
Chapter 5. Formulation and solution strategies
5.1. Review of field equations
5.2. Boundary conditions and fundamental problem classifications
5.3. Stress formulation
5.4. Displacement formulation
5.5. Principle of superposition
5.6. Saint–Venant's principle
5.7. General solution strategies
5.8. Singular elasticity solutions
Chapter 6. Strain energy and related principles
6.1. Strain energy
6.2. Uniqueness of the elasticity boundary-value problem
6.3. Bounds on the elastic constants
6.4. Related integral theorems
6.5. Principle of virtual work
6.6. Principles of minimum potential and complementary energy
6.7. Rayleigh–Ritz method
Chapter 7. Two-dimensional formulation
7.1. Plane strain
7.2. Plane stress
7.3. Generalized plane stress
7.4. Antiplane strain
7.5. Airy stress function
7.6. Polar coordinate formulation
Chapter 8. Two-dimensional problem solution
8.1. Cartesian coordinate solutions using polynomials
8.2. Cartesian coordinate solutions using Fourier methods
8.3. General solutions in polar coordinates
8.4. Example polar coordinate solutions
8.5. Simple plane contact problems
Chapter 9. Extension, torsion, and flexure of elastic cylinders
9.1. General formulation
9.2. Extension formulation
9.3. Torsion formulation
9.4. Torsion solutions derived from boundary equation
9.5. Torsion solutions using Fourier methods
9.6. Torsion of cylinders with hollow sections
9.7. Torsion of circular shafts of variable diameter
9.8. Flexure formulation
9.9. Flexure problems without twist
Part 2. Advanced applications
Chapter 10. Complex variable methods
10.1. Review of complex variable theory
10.2. Complex formulation of the plane elasticity problem
10.3. Resultant boundary conditions
10.4. General structure of the complex potentials
10.5. Circular domain examples
10.6. Plane and half-plane problems
10.7. Applications using the method of conformal mapping
10.8. Applications to fracture mechanics
10.9. Westergaard method for crack analysis
Chapter 11. Anisotropic elasticity
11.1. Basic concepts
11.2. Material symmetry
11.3. Restrictions on elastic moduli
11.4. Torsion of a solid possessing a plane of material symmetry
11.5. Plane deformation problems
11.6. Applications to fracture mechanics
11.7. Curvilinear anisotropic problems
Chapter 12. Thermoelasticity
12.1. Heat conduction and the energy equation
12.2. General uncoupled formulation
12.3. Two-dimensional formulation
12.4. Displacement potential solution
12.5. Stress function formulation
12.6. Polar coordinate formulation
12.7. Radially symmetric problems
12.8. Complex variable methods for plane problems
Chapter 13. Displacement potentials and stress functions: Applications to three-dimensional problems
13.1. Helmholtz displacement vector representation
13.2. Lamé's strain potential
13.3. Galerkin vector representation
13.4. Papkovich–Neuber representation
13.5. Spherical coordinate formulations
13.6. Stress functions
Chapter 14. Nonhomogeneous elasticity
14.1. Basic concepts
14.2. Plane problem of a hollow cylindrical domain under uniform pressure
14.3. Rotating disk problem
14.4. Point force on the free surface of a half-space
14.5. Antiplane strain problems
14.6. Torsion problem
Chapter 15. Micromechanics applications
15.1. Dislocation modeling
15.2. Singular stress states
15.3. Elasticity theory with distributed cracks
15.4. Micropolar/couple-stress elasticity
15.5. Elasticity theory with voids
15.6. Doublet mechanics
15.7. Higher gradient elasticity theories
Chapter 16. Numerical finite and boundary element methods
16.1. Basics of the finite element method
16.2. Approximating functions for two-dimensional linear triangular elements
16.3. Virtual work formulation for plane elasticity
16.4. FEM problem application
16.5. FEM code applications
16.6. Boundary element formulation
Appendix A. Basic field equations in Cartesian, cylindrical, and spherical coordinates
Appendix B. Transformation of field variables between Cartesian, cylindrical, and spherical components
Appendix C. MATLAB® Primer
Appendix D. Review of mechanics of materials
Index

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